Theorems · Theorem · complex analysis
Real.sum_le_exp_of_nonneg
∀ {x : ℝ}, 0 ≤ x → ∀ (n : ℕ), ∑ i ∈ Finset.range n, x ^ i / ↑i.factorial ≤ Real.exp x- Defined in
- Mathlib.Analysis.Complex.Exponential
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Complexproof · cited by 5,565
- Finset.sumstatement and proof · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
- absproof · cited by 1,814
- Complex.ofRealproof · cited by 1,654
- Finset.rangestatement and proof · cited by 1,341
- Complex.reproof · cited by 882
- Real.expstatement · cited by 871
- Nat.factorialstatement and proof · cited by 616
- Nat.cast_pos'proof · cited by 219
- CauSeqproof · cited by 189
Cited by5
Results whose statement or proof uses this declaration.
- Complex.norm_exp_sub_sum_le_exp_norm_sub_sumproof · cited by 1
- Real.one_half_lt_eulerMascheroniSeq_sixproof · cited by 1
- Complex.norm_exp_sub_sum_le_norm_mul_expproof · cited by 0
- Real.quadratic_le_exp_of_nonnegproof · cited by 0
- Real.pow_div_factorial_le_expproof · cited by 0